Clases del componente: Funcionalidades

Cells with trapped bodies

The behaviour of the flow generated by the flagella when the cell body is fixed is the same for D.

salinaas it is with C. reinhardtii. That is, we observe large lateral eddies that pull the surrounding fluid close to the body with the higher magnitude flows focused upon the region close to the flagella, see Figure 4.16. However, the vortices lie closer to the D. salina cell body, which is likely a consequence of the flagellar beat being more focused along the sides of the body.

(a) (b)

Figure 4.16: Flow fields for two examples of trapped D. salina. The cells are trapped between glass slide and cover-slip, but their flagella are free to beat. Flow fields are constructed using the PIV software MatPIV [113]. (a) The flow fields are averaged over 1000 frames. The cell’s anterior end is pointing northward, where north is toward the top of the page. (b) The velocity fields are averaged over 1300 frames and the cell is pointing north-west.

Figure 4.17 displays the decay of the flow velocity for the cells in Figure 4.16 and we observe local minima along the lateral curves just as we did for the C. reinhardtii cells; the local minimum that occurs along the posterior end is most likely due to noise, as we can see that in Figures 4.16(b) the flow field is sporadic away from the cell. Comparing with the C. reinhardtii observations we also see that there is a greater drop in magnitude in the near field with D. salina, which again can be attributed to the flagellar extension being less with the D. salina cell.

Free-swimming cells

A typical trajectory over a single beat is shown in Figure 4.18(a). The trajectories are similar to C.

reinhardtii in that we observe distinct behaviour during the effective and recovery stroke. However

10⁰ 10¹

Figure 4.17: The decay of the mean flow velocity magnitude, | hui |, as a function of radial distance, r/R, where R is the length of the cell’s semi-minor axis. The data corresponds to the flow fields in Figure 4.16 and has been computed through four directions. The solid and dashed lines are shown for visualisation purposes and have gradients of −2 and −1 respectively.

D. salina tend to have flagellar beats that are mostly asynchronous and the result is that we see a lot of wiggling of the cell body, which is reflected in the trajectories when φ₀ = −5π/36 and φ₀= 10π/9. Note that with respect to the Cartesian axis defined in Chapter 2, k points out of the page and the initial orientation of the experimental swimmers is in the xy-plane; θ₀ = ψ₀= π/2.

−0.20 −0.1 0 0.1 0.2

Figure 4.18: (a) Trajectories over the course of a single beat for three experimental observations of swimming D.

salina. (b) The behaviour of the swimming speed along the x-axis, solid line, and y-axis,dashedline, over a number of beats. Here we have identified a region where we have a period of synchronous swimming followed by a period of asynchronous swimming. During the asymmetric beat the magnitude of the instantaneous velocity is increased.

After the asynchronous beat we observe a period where the cell is rotating out of the plane.

The asynchrony of the D. salina flagellar beat can be observed in the swimming speed as a function of time plot in Figure 4.18(b). Through beats 35–37 we observe symmetry between flagella, whereas between beats 37–38 the flagella beat asymmetrically and as a consequence we observe large spikes in the velocity. The mean velocity over the beat is U = (0.0331, 0.0349) d b⁻¹, over twice the speed along the x-axis observed for the preceding symmetric beat. Furthermore, the asynchronous beat actually causes the cell to rotate out of the plane and consequently we observe

a different trend in the behaviour which follows it (see beats 38–40 in Figure 4.18(b)).

In Figure 4.19 the swimming speed versus time curves are shown for the same cell that produced the trajectories in Figure 4.18(a). For the individual swimmers we see that like C. reinhardtii there are positive swimming speeds during the effective stroke followed by a period where the cell is displaced backward along its principal axis. This is clearer in Figure 4.19(a) when the two flagella beat at the same frequency. When the flagellar beat is slightly asymmetric the swimming speed time curves are less clear. For all images the solid anddashedlines show the swimming speed along the x- and y- axes, respectively.

0 0.2 0.4 0.6 0.8 1

Figure 4.19: The swimming speed over the course of a single beat for three individual cells. The speeds are derived from the trajectories in 4.18(a). The solid and dashed-lines show the swimming speed along the x- and y- axes, respectively.

Observations of flagellar beating

Although both Chlamydomonas and Dunaliella are bi-flagellates the flagellar beats are different for both types of algae. For Chlamydomonas we observe a breast-stroke like motion. For Dunaliella we observe that during the effective stroke bending waves move the flagella toward the posterior of the cell. During the recovery stroke the flagella are restored to their initial position by the same bending wave. A typical stroke for D. salina is shown in Figure 4.20, where we can see that as with Chlamydomonasthe two strokes are not distinct. Furthermore, we can see that the flagella extend further towards the posterior end and closer to the cell body during the recovery stroke and extend further in the direction of the cell’s minor-axis during the effective stroke than is generally observed with Chlamydomonas. For the majority of the time D. salina exhibit asynchronous flagellar beats, one flagellum beats with a greater frequency than the other [109].

It is also common for species of Dunaliella to have flagella slightly longer than their cell body.

In the case of D. salina the flagella can be as large as 1.5 times the body length [14].

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)

Figure 4.20: Images detailing the flagellar positions for a typical flagellar beat for D. salina. The beat is distinct from other bi-flagellates like Chlamydomonas.